Agreed on the bagging. When I got the occasional one (we had a relative with us sometimes that needed them) and would use it, I would bag and then dig in the trash and put it towards the middle of the trash.

I always bagged my disposables when I was using them. I would triple bag them with those plastic grocery bags after rolling it up and taping it to itself.
Now I use cloth diapers, but I still have to clean them out whenever I mess, so I put the mess and the paper towels into the same set-up, 3 grocery bags. It still makes the trash smell like a sewer, but not as bad as it could be.
And speaking of the dogs getting it! I live out in the country on 4 acres, and my main trash can is out beside the electric pole, about 30 feet from the back door. Whenever I have a bag to throw away at night, I'll just turn on the outside light and toss it towards the can. I usually get real close, and then in the morning, I'll go out and put it inside the can. My dig stays in the house, so I don't need to worry about that. Well, one night I guess one of my neighbor's dogs got into my yard and found one of the bags, and it was all over the yard. Chewed up paper towels with poop on them, and the plastic bags laying beside it. But I guess it didn't taste too good to the dog, because after that first one, they never tore into another, and they've had plenty of chances too!